Question

Measurements show that the pH of a particular lake is 4.0. What is the hydrogen ion concentration of the lake?

(A) 4.0 M

(B) 10^-10 M

(C) 10^-4 M

(D) 10⁴ M

Short answer

(A) The option “\(4.0{\rm{ M}}\)” is false.

(B) The option “\({10^{ - 10}}{\rm{ M}}\)” is false.

(C) The option “\({10^{ - 4}}{\rm{ M}}\)” is true.

(D) The option “\({10^4}{\rm{ M}}\)” is false.

Step-by-step solution

Potential of hydrogen

The potential of hydrogen (pH) is the degree of alkalinity or acidity in a solution and is also a unit of the hydrogen ion concentration. A higher pH indicates a lower concentration of hydrogen ions, and a lower pH indicates a higher concentration.

Explanation for option‘(A)’

The formula for calculating pH is as follows:

\({\rm{pH}} = - \log [{{\rm{H}}^{\rm{ + }}}]\)

Putting the value of the hydrogen ion concentration in the above formula gives the value of pH.

\(\begin{aligned}{\rm{pH}} &= - \log [{{\rm{H}}^{\rm{ + }}}]\\ &= - \log [4.0{\rm{ M}}]\\ &= - 0.602\end{aligned}\)

The pH value of the lake water, with hydrogen ion concentration of \(4.0{\rm{ M}}\), is \( - 0.602\).

Thus, thepH will not be 4.0 if the hydrogen ion concentration is\(4.0{\rm{ M}}\).

Therefore, the given statement is false.

Explanation for option ‘(B)’

The formula for calculating pH is as follows:

\({\rm{pH}} = - \log [{{\rm{H}}^{\rm{ + }}}]\)

Putting the value of the hydrogen ion concentration in the above formula gives the value of pH.

\(\begin{aligned}{\rm{pH}} &= - \log [{{\rm{H}}^{\rm{ + }}}]\\ &= - \log [{10^{ - 10}}{\rm{ M}}]\\ &= 10\end{aligned}\)

The pH value of the lake water, with hydrogen ion concentration of \({10^{ - 10}}{\rm{ M}}\), is \(10\).

Thus, the pH will not be 4.0 if the hydrogen ion concentration is\({10^{ - 10}}{\rm{ M}}\).

Therefore, the given statement is false.

Explanation for option ‘(C)’

It is given that the water of the lake has a pHof \(4\). The formula for calculating \({{\rm{H}}^{\rm{ + }}}\)concentration is as follows:

\([{{\mathop{\rm H}\nolimits} ^ + }] = {10^{ - {\rm{pH}}}}\)

By putting the given value of pH in the above formula, the \({{\rm{H}}^{\rm{ + }}}\) concentration can be calculated.

\(\begin{aligned}[{{\mathop{\rm H}\nolimits} ^ + }] &= {10^{ - 4}}\\ &= {10^{ - 4}}{\rm{ M}}\end{aligned}\)

Thus, the pH will be 4.0 if the hydrogen ion concentration is\({10^{ - 4}}{\rm{ M}}\).

Therefore, the given statement is true.

Explanation for option ‘(D)’

The formula for calculating pH is as follows:

\({\rm{pH}} = - \log [{{\rm{H}}^{\rm{ + }}}]\)

Putting the value of hydrogen ion concentration in the above formula gives the value of pH.

\(\begin{aligned}{\rm{pH}} &= - \log [{{\rm{H}}^{\rm{ + }}}]\\ &= - \log [{10^4}{\rm{ M}}]\\ &= - 4\end{aligned}\)

The pH value of the lake water, with hydrogen ion concentration of \({10^4}{\rm{ M}}\), is \( - 4\).

Thus, the pH will be 4.0 if the hydrogen ion concentration is\({10^4}{\rm{ M}}\).

Therefore, the given statement is false.